How to Make It
Place tomatoes in a medium bowl; sprinkle with salt and ground pepper, and toss to combine. Add shallot, oil, vinegar, and garlic; toss well. Let stand at room temperature at least 20 minutes.
Meanwhile, cook pasta in salted water according to package directions. Reserve 1 cup cooking liquid; drain pasta.
Place 2 prosciutto slices on paper towels on a microwave-safe plate. Microwave on HIGH until crisp, 1 minute and 30 seconds to 2 minutes. Repeat with remaining 2 prosciutto slices.
Drain tomato mixture over a bowl, reserving liquid. Combine warm pasta, anchovies, tomato liquid, and 1/3 cup cooking liquid in a large skillet over medium-high. Cook until sauce slightly thickens and coats pasta, about 2 minutes. Remove from heat. Stir in drained tomato mixture, sliced basil, olives, oregano, and capers. Crumble prosciutto over pasta; garnish with basil leaves and, if desired, cracked pepper.